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A mild steel wire is 10 mm in diameter and 1 m long. If the wire is subjected to an axial tensile load 10 kN, find an extension of the road (Take E = 200 × 109 Pa) :
- a)0.55 mm
- b)0.10 mm
- c)0.64 mm
- d)0.75 mm
Correct answer is option 'C'. Can you explain this answer?
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A mild steel wire is 10 mm in diameter and 1 m long. If the wire is su...
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A mild steel wire is 10 mm in diameter and 1 m long. If the wire is su...
To find the extension of the road, we can use Hooke's Law, which states that the extension of a material is directly proportional to the applied force.
Hooke's Law can be written as:
F = k * ΔL
Where:
F is the force applied (10 kN)
k is the spring constant (also known as Young's modulus, E)
ΔL is the change in length (extension) of the wire
We are given the diameter of the wire, so we can calculate the radius (r) using the formula:
r = diameter / 2
r = 10 mm / 2 = 5 mm = 0.005 m
The cross-sectional area of the wire (A) can be calculated using the formula:
A = π * r^2
A = π * (0.005 m)^2 = 0.00007854 m^2
Now, we can find the spring constant (E) using the formula:
E = (F * L) / (A * ΔL)
Rearranging the formula to solve for ΔL:
ΔL = (F * L) / (A * E)
Plugging in the given values:
ΔL = (10 kN * 1 m) / (0.00007854 m^2 * 200 GPa)
Converting the force to Newton:
10 kN = 10,000 N
Converting the Young's modulus to Pascal:
200 GPa = 200,000,000,000 Pa
Plugging in the converted values:
ΔL = (10,000 N * 1 m) / (0.00007854 m^2 * 200,000,000,000 Pa)
Calculating the result:
ΔL = 0.006369 m
Therefore, the extension of the road (wire) is approximately 0.006369 meters.
Hooke's Law can be written as:
F = k * ΔL
Where:
F is the force applied (10 kN)
k is the spring constant (also known as Young's modulus, E)
ΔL is the change in length (extension) of the wire
We are given the diameter of the wire, so we can calculate the radius (r) using the formula:
r = diameter / 2
r = 10 mm / 2 = 5 mm = 0.005 m
The cross-sectional area of the wire (A) can be calculated using the formula:
A = π * r^2
A = π * (0.005 m)^2 = 0.00007854 m^2
Now, we can find the spring constant (E) using the formula:
E = (F * L) / (A * ΔL)
Rearranging the formula to solve for ΔL:
ΔL = (F * L) / (A * E)
Plugging in the given values:
ΔL = (10 kN * 1 m) / (0.00007854 m^2 * 200 GPa)
Converting the force to Newton:
10 kN = 10,000 N
Converting the Young's modulus to Pascal:
200 GPa = 200,000,000,000 Pa
Plugging in the converted values:
ΔL = (10,000 N * 1 m) / (0.00007854 m^2 * 200,000,000,000 Pa)
Calculating the result:
ΔL = 0.006369 m
Therefore, the extension of the road (wire) is approximately 0.006369 meters.
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A mild steel wire is 10 mm in diameter and 1 m long. If the wire is subjected to an axial tensile load 10 kN, find an extension of the road (Take E = 200 × 109Pa) :a)0.55 mmb)0.10 mmc)0.64 mmd)0.75 mmCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A mild steel wire is 10 mm in diameter and 1 m long. If the wire is subjected to an axial tensile load 10 kN, find an extension of the road (Take E = 200 × 109Pa) :a)0.55 mmb)0.10 mmc)0.64 mmd)0.75 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mild steel wire is 10 mm in diameter and 1 m long. If the wire is subjected to an axial tensile load 10 kN, find an extension of the road (Take E = 200 × 109Pa) :a)0.55 mmb)0.10 mmc)0.64 mmd)0.75 mmCorrect answer is option 'C'. Can you explain this answer?.
A mild steel wire is 10 mm in diameter and 1 m long. If the wire is subjected to an axial tensile load 10 kN, find an extension of the road (Take E = 200 × 109Pa) :a)0.55 mmb)0.10 mmc)0.64 mmd)0.75 mmCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A mild steel wire is 10 mm in diameter and 1 m long. If the wire is subjected to an axial tensile load 10 kN, find an extension of the road (Take E = 200 × 109Pa) :a)0.55 mmb)0.10 mmc)0.64 mmd)0.75 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mild steel wire is 10 mm in diameter and 1 m long. If the wire is subjected to an axial tensile load 10 kN, find an extension of the road (Take E = 200 × 109Pa) :a)0.55 mmb)0.10 mmc)0.64 mmd)0.75 mmCorrect answer is option 'C'. Can you explain this answer?.
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